Problem: Simplify the following expression: $\sqrt{11}-\sqrt{44}+\sqrt{275}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{11}-\sqrt{44}+\sqrt{275}$ $= \sqrt{11}-\sqrt{4 \cdot 11}+\sqrt{25 \cdot 11}$ Separate the radicals and simplify. $= \sqrt{11}-\sqrt{4} \cdot \sqrt{11}+\sqrt{25} \cdot \sqrt{11}$ $= \sqrt{11}-2\sqrt{11}+5\sqrt{11}$ Finally, simplify by combining the terms. $= ( 1 - 2 + 5 )\sqrt{11} = 4\sqrt{11}$